Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Does the following inequality holds for every POSITIVE 'x' ?

  1. Aug 13, 2010 #1
    does the following inequality holds for every POSITIVE 'x' ?

    [tex] e^{-x}-1\le Cx^{1/4+e} [/tex] here 'C' and e are positive constants

    i think that for very very small 'e' the constant must be very BIG but no other hint i find
  2. jcsd
  3. Aug 13, 2010 #2


    User Avatar
    Science Advisor

    Re: inequality

    Certainly not without additional restrictions on e and C. (You should not use 'e' as a variable name to avoid confusion with e = 2.71...)

    However, if e >= 1, the left hand side is non-positive, so in that case the equation words.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook